For several reasons:

1. Bike wheel rims get dirty and wet when riding (especially off road). A dirty wet rim doesn't work as a friction surface very well. Because discs are near the hub, they avoid most of the spashback and remain cleaner.
2. Bike wheel rims are made of thin aluminum. You can't press too hard on a wheel rim or it will bend or tear. Brake discs are made of thick steel, and can withstand a lot higher loads without breaking.
3. Because of the steel disk, you can use a more aggressive brake pad. Rim brakes have rubber friction pads, while disc brakes have ceramic pads which create a lot more friction. Using ceramic pads on a rim would quickly destroy the delicate aluminum.

Rim breaking actually has a mechanical advantage, being closer to outside of the wheel gives it a longer moment arm and more stopping power for the same applied friction force. But the fact that rims are so delicate means you can't use very much friction force, while a disc brake can withstand much higher load.s